Spectra of evolution operators of a class of neutral renewal equations: Theoretical and numerical aspects

In this work we begin a theoretical and numerical investigation on the spectra of evolution operators neutral renewal equations, with stability equilibria periodic orbits in mind. We start from simplest form linear equation one discrete delay fully characterize spectrum its monodromy operator. perform experiments discretizing via pseudospectral collocation, confirming results giving perspectives generalization to systems multiple delays. Although do not attempt rigorous analysis method, give some considerations possible approach problem.